Results 1  10
of
34
Epidemics in Partially Overlapped Multiplex Networks
, 2014
"... Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a different topology. In realworld networks, however, not all nod ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a different topology. In realworld networks, however, not all nodes are present on every layer. To generate a more realistic scenario, we use a generalized multiplex network and assume that only a fraction q of the nodes are shared by the layers. We develop a theoretical framework for a branching process to describe the spread of an epidemic on these partially overlapped multiplex networks. This allows us to obtain the fraction of infected individuals as a function of the effective probability that the disease will be transmitted T. We also theoretically determine the dependence of the epidemic threshold on the fraction qw0 of shared nodes in a system composed of two layers. We find that in the limit of q?0 the threshold is dominated by the layer with the smaller isolated threshold. Although a system of two completely isolated networks is nearly indistinguishable from a system of two networks that share just a few nodes, we find that the presence of these few shared nodes causes the epidemic threshold of the isolated network with the lower propagating capacity to change discontinuously and to acquire the threshold of the other network.
Structural reducibility of multilayer networks
, 2015
"... Many complex systems can be represented as networks consisting of distinct types of interactions, which can be categorized as links belonging to different layers. For example, a good description of the full protein–protein interactome requires, for some organisms, up to seven distinct network layers ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Many complex systems can be represented as networks consisting of distinct types of interactions, which can be categorized as links belonging to different layers. For example, a good description of the full protein–protein interactome requires, for some organisms, up to seven distinct network layers, accounting for different genetic and physical interactions, each containing thousands of protein–protein relationships. A fundamental open question is then how many layers are indeed necessary to accurately represent the structure of a multilayered complex system. Here we introduce a method based on quantum theory to reduce the number of layers to a minimum while maximizing the distinguishability between the multilayer network and the corresponding aggregated graph. We validate our approach on synthetic benchmarks and we show that the number of informative layers in some real multilayer networks of protein–genetic interactions, social, economical and transportation systems can be reduced by up to 75%.
MuxViz: a tool for multilayer analysis and visualization of networks
, 2014
"... Multilayer relationships among entities and information about entities must be accompanied by the means to analyse, visualize and obtain insights from such data. We present opensource software (muxViz) that contains a collection of algorithms for the analysis of multilayer networks, which are an im ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Multilayer relationships among entities and information about entities must be accompanied by the means to analyse, visualize and obtain insights from such data. We present opensource software (muxViz) that contains a collection of algorithms for the analysis of multilayer networks, which are an important way to represent a large variety of complex systems throughout science and engineering. We demonstrate the ability of muxViz to analyse and interactively visualize multilayer data using empirical genetic, neuronal and transportation networks. Our software is available at
ARTICLE Multiple tipping points and optimal repairing in interacting networks
"... Systems composed of many interacting dynamical networkssuch as the human body with its biological networks or the global economic network consisting of regional clustersoften exhibit complicated collective dynamics. Three fundamental processes that are typically present are failure, damage spread ..."
Abstract
 Add to MetaCart
Systems composed of many interacting dynamical networkssuch as the human body with its biological networks or the global economic network consisting of regional clustersoften exhibit complicated collective dynamics. Three fundamental processes that are typically present are failure, damage spread and recovery. Here we develop a model for such systems and find a very rich phase diagram that becomes increasingly more complex as the number of interacting networks increases. In the simplest example of two interacting networks we find two critical points, four triple points, ten allowed transitions and two 'forbidden' transitions, as well as complex hysteresis loops. Remarkably, we find that triple points play the dominant role in constructing the optimal repairing strategy in damaged interacting systems. To test our model, we analyse an example of real interacting financial networks and find evidence of rapid dynamical transitions between welldefined states, in agreement with the predictions of our model.
A Critical Review of Robustness in Power Grids Using Complex Networks Concepts
 ENERGIES
, 2015
"... ..."
TIME CENTRALITY IN DYNAMIC COMPLEX NETWORKS
"... There is an everincreasing interest in investigating dynamics in timevarying graphs (TVGs). Nevertheless, so far, the notion of centrality in TVG scenarios usually refers to metrics that assess the relative importance of nodes along the temporal evolution of the dynamic complex network. For some ..."
Abstract
 Add to MetaCart
(Show Context)
There is an everincreasing interest in investigating dynamics in timevarying graphs (TVGs). Nevertheless, so far, the notion of centrality in TVG scenarios usually refers to metrics that assess the relative importance of nodes along the temporal evolution of the dynamic complex network. For some TVG scenarios, however, more important than identifying the central nodes under a given node centrality definition is identifying the key time instants for taking certain actions. In this paper, we thus introduce and investigate the notion of time centrality in TVGs. Analogously to node centrality, time centrality evaluates the relative importance of time instants in dynamic complex networks. In this context, we present two time centrality metrics related to diffusion processes. We evaluate the two defined metrics using both a realworld dataset representing an inperson contact dynamic network and a synthetically generated randomized TVG. We validate the concept of time centrality showing that diffusion starting at the best ranked time instants (i.e. the most central ones), according to our metrics, can perform a faster and more efficient diffusion process.
NonNegative Matrix Factorizations for Multiplex Network Analysis
"... AbstractNetworks have been a general tool for representing, analyzing, and modeling relational data arising in several domains. One of the most important aspect of network analysis is community detection or network clustering. Until recently, the major focus have been on discovering community stru ..."
Abstract
 Add to MetaCart
(Show Context)
AbstractNetworks have been a general tool for representing, analyzing, and modeling relational data arising in several domains. One of the most important aspect of network analysis is community detection or network clustering. Until recently, the major focus have been on discovering community structure in single (i.e., monoplex) networks. However, with the advent of relational data with multiple modalities, multiplex networks, i.e., networks composed of multiple layers representing different aspects of relations, have emerged. Consequently, community detection in multiplex network, i.e., detecting clusters of nodes shared by all layers, has become a new challenge. In this paper, we propose Network Fusion for Composite Community Extraction (NFCCE), a new class of algorithms, based on four different nonnegative matrix factorization models, capable of extracting composite communities in multiplex networks. Each algorithm works in two steps: first, it finds a nonnegative, lowdimensional feature representation of each network layer; then, it fuses the feature representation of layers into a common nonnegative, lowdimensional feature representation via collective factorization. The composite clusters are extracted from the common feature representation. We demonstrate the superior performance of our algorithms over the stateoftheart methods on various types of multiplex networks, including biological, social, economic, citation, phone communication, and brain multiplex networks.